THE LANGEVIN MONTE CARLO ALGORITHM IN THE NON-SMOOTH LOG-CONCAVE CASE

• 成果类型: Article
• 署名作者: Lehec, Joseph
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Poitiers
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1935
• 发表日期: 2023
• 页码: 4858-4874
• 关键词: convex-bodies

摘要

We prove nonasymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of affine functions on an arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz, in contrast with most existing works on the topic.